Related reflections to the axioms of separation in semigroups with topologies and some applications

TL;DR

This paper investigates how topological and semitopological semigroups relate to separation axioms and explores conditions for topological semigroups to possess the Souslin property, with applications in topology.

Contribution

It introduces reflections of semigroup categories onto spaces satisfying various separation axioms and applies these to identify conditions for the Souslin property in topological semigroups.

Findings

Characterization of reflections onto T0, T1, T2, T3, and regular spaces.

Conditions under which topological semigroups have the Souslin property.

Applications of reflection properties to topological semigroup theory.

Abstract

In this paper we study the reflections of the category of topological and semitopological semigroups on the category of the class of topological spaces satisfying separation axioms $T_{0}$, $T_{1}$, $T_{2}$, $T_{3}$ and regular and we apply its properties for to find conditions under which a topological semigroup has the Souslin property.